MMP for Enriques pairs and singular Enriques varieties

Francesco Denisi (Institut de Mathématiques de Jussieu)

Tuesday 26th November 15:00-16:00 Maths 311B

Abstract

An Enriques manifold is a connected complex manifold that is not simply connected and whose universal covering is an irreducible holomorphic symplectic (IHS) manifold. Given a projective IHS manifold X and an effective R-divisor D such that the pair (X,D) is log canonical, Lehn and Pacienza proved that any MMP starting from (X,D) terminates. The goal of this talk is twofold. First, we discuss an analogous result for Enriques pairs, which we define as log canonical pairs (Y, D), where Y is an Enriques manifold and D is an effective R-divisor. Second, we characterize the underlying variety of the resulting minimal model (Y’, D’) of (Y,D). This leads naturally to the definition of primitive Enriques varieties, for which we provide examples and explore some of their properties. The talk is based on joint work with Á. D. Ríos Ortiz, N. Tsakanikas and Z. Xie.

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